The esc, motor, and the battery are matched to each other and the task. The most important considerations are voltage and current and power. The esc uses a "speed / position" signal from the receiver, and its power and common line (3 wires). Your rudder control would use a position servo, probably the car had one for steering. The thrust motor also needs speed control, but the car has no real equivalent of that second motor speed control. The radio system may not have a spare proportional channel for that. Also the drive motor and servo in the car may be too small for your needs. This depends on the size of the hovercraft.
Generally the radio control system has several channels, meaning control channels not radio channels. These are classified as:
a) proportional channels (for speed/position control, adjustable or variable like the esc and the rudder.
b) on/off channels that are just switched on or off.
It seems like you need 3 proportional channels: two for thrust and lift motors (2 x esc) and one for rudder servo. More or less any speed or position servo can be connected to proportional channels. However the radio might have different outputs that suit larger servos (using the direct battery voltage 6V). There are different connectors for different brands. The esc may use a separate external battery for the motor. The radio system may use its own battery of nominal 5 to 6V. The radio battery can be replaced by a battery eliminator (BEC), which converts the external battery to 5-6V so no separate battery needed.
This link shows how just one motor, battery, esc, receiver and BEC are connected. You will see a red wire disconnected. That is because this particular esc uses the full battery voltage (it doesn't need a separate 5V supply from the radio). Some position servos can use a 6V motor supply, and a 5V electronics supply from the receiver. The receiver runs directly from a 6V battery and provides a 5V regulator internally. When using a higher voltage battery there might be 2 different BECs used for this situation.
http://rc.runryder.com/helicopter/gallery/64200/ccbec_wiring.jpg
It sounds like you have followed this concept. However the esc and motor for the car may have just run from the 6V radio battery. Maybe you are using a different esc and motor? Look at a tester for esc or servos. This is cheap and simple. It rovides a test signal to change the motor speed or servo position.
http://www.555-timer-circuits.com/servo-tester.html